Stress-Strain-Time Behavior

In this general approach to viscoelasticity, appropriate models are constructed for the interpretation of the stress-strain-time behavior of a polymer. Then, values of Young s modulus G of the elastic elements and the viscosities i] of the viscous elements are used to characterize and predict the general behavior of the material. 

Hirst, T.J. 1968. The influence of compositionalfactorson the stress-strain-time behavior of soils. PhD Thesis, University of California, Berkeley, CA. 

In order to understand the thermomechanical cycle of the syntactic foam under different test conditions better, the test results are presented in both 3-D and 2-D format. Typical 2-D axial stress-time and temperature-time curves for the foam confined by the nylon liner, programmed at 79 °C, and under 60% pre-strain level, and fully confined shape recovery are shown in Figure 3.29. Typical 3-D axial stress-axial strain-ternperamre thermomechanical cycles for the syntactic foam at a programming ternperamre of 71 °C, pre-strain level of 30%, and fully confined shape recovery are shown in Figure 3.30. Typical 3-D axial stress-axial strain-time behaviors at a programming temperature of 79 °C, pre-strain level of 30%, and fully confined shape recovery are shown in Figure 3.31. 

The extremely nonlinear behaviors for the entire thermomechanical cycle, including a three-step glassy temperature programming process and one-step heating recovery in both the stress-strain-time view and stress-strain-temperature view, are shown in Figure 3.38 (a) and (b). 

Figure 5.12 Thermomechanical behavior of SMPFs by both cold and hot tension programmings, (a) Stress-strain-time diagram for Sample 2. Steps 1 to 5 complete programming and Step 6 completes stress recovery, where step 1 is to stretch the fiber bundle to 100% strain at a rate of200 ram/min at 100 °C step 2 is to hold the strain constant for 1 hour step 3 is to cool the fiber to room temperature slowly while holding the pre-strain constant step 4 is to release the fiber bundle from tbe fixture (unloading) step 5 is to relax the fiber in the stress-free condition until the shape is fixed and step 6 is to recover the fiber at 150 °C in the fully constrained condition (adapted from Reference [20]) (b) Stress-strain-time diagram for Sample 3. Steps 1-4 complete programming and step 5 completes stress recovery, where step 1 is to stretch the fiber bundle to 100% strain at a rate of 200 mm/min at room temperature step 2 is to hold the strain constant for 1 hour step 3 is to release the fiber bundle from fixtures (unloading) step 4 is to relax the fiber in the stress-free condition until the shape is fixed and step 5 is to recover the fiber at 150 °C in the fully constrained condition (adapted from Reference [20]) (c) Stress evolution with time for Sample 2 (d) Stress evolution with time for Sample 3.

If a body were subjected to a number of varying deformation cycles, a complex time dependent stress would result. If the viscoelastic behavior is linear, this complex stress-strain-time relation is reduced to a simple scheme by the superposition principle proposed by Boltzmann. This... 

It is important to differentiate between brittie and plastic deformations within materials. With brittie materials, the behavior is predominantiy elastic until the yield point is reached, at which breakage occurs. When fracture occurs as a result of a time-dependent strain, the material behaves in an inelastic manner. Most materials tend to be inelastic. Figure 1 shows a typical stress—strain diagram. The section A—B is the elastic region where the material obeys Hooke s law, and the slope of the line is Young s modulus. C is the yield point, where plastic deformation begins. The difference in strain between the yield point C and the ultimate yield point D gives a measure of the brittieness of the material, ie, the less difference in strain, the more brittie the material. 

Typical patterns of stress—strain behavior and the relationship of molecular motion on stress—strain behavior have been discussed (10,18,19,21,49—51). At times, it becomes desirable to characterize stress—strain behavior numerically so that a large amount of information can be condensed and many fibers exhibiting different behaviors can be compared. Procedures for measurement of stress—strain parameters are described ia ASTMD3822 andD2101 (10). 

Wave profiles in the elastic-plastic region are often idealized as two distinct shock fronts separated by a region of constant elastic strain. Such an idealized behavior is seldom, if ever, observed. Near the leading elastic wave, relaxations are typical and the profile in front of the inelastic wave typically shows significant changes in stress with time. 

As an example, for room-temperature applications most metals can be considered to be truly elastic. When stresses beyond the yield point are permitted in the design, permanent deformation is considered to be a function only of applied load and can be determined directly from the stress-strain diagram. The behavior of most plastics is much more dependent on the time of application of the load, the past history of loading, the current and past temperature cycles, and the environmental conditions. Ignorance of these conditions has resulted in the appearance on the market of plastic products that were improperly designed. Fortunately, product performance has been greatly improved as the amount of technical information on the mechanical properties of plastics has increased in the past half century. More importantly, designers have become more familiar with the behavior of plastics rather than... 

Long time dynamic load involves behaviors such as creep, fatigue, and impact. T vo of the most important types of long-term material behavior are more specifically viscoelastic creep and stress relaxation. Whereas stress-strain behavior usually occurs in less than one or two hours, creep and stress relaxation may continue over the entire life of the structure such as 100,000 hours or more. 

When a viscoelastic material is subjected to a constant stress, it undergoes a time-dependent increase in strain. This behavior is called creep. The viscoelastic creep behavior typical of many TPs is illustrated in Figs. 2-22 and 2-23. At time to the material is suddenly subjected to a constant stress that is main-... 

Fig. 2-22 Viscoelastic creep behavior typical of many TPs under long-term stress to rupture (a) input stress vs. time profile and (b) output strain vs. time profile.

When a viscoelastic material is subjected to a constant strain, the stress initially induced within it decays in a time-dependent manner. This behavior is called stress relaxation. The viscoelastic stress relaxation behavior is typical of many TPs. The material specimen is a system to which a strain-versus-time profile is applied as input and from which a stress-versus-time profile is obtained as an output. Initially the material is subjected to a constant strain that is maintained for a long period of time. An immediate initial stress gradually approaches zero as time passes. The material responds with an immediate initial stress that decreases with time. When the applied strain is removed, the material responds with an immediate decrease in stress that may result in a change from tensile to compressive stress. The residual stress then gradually approaches zero. 

Creep rupture. Creep-rupture data are obtained in the same way as creep data except that higher stresses are used and the time is measured to failure (Figs. 2-28 and 29). The strains are sometimes recorded, but this is not necessary for creep rupture. The results are generally plotted as the log stress versus log time to failure (110). In creep-rupture tests it is the material s behavior just prior to the rupture that is of primary interest. In these tests a number of samples are subjected to different levels of constant stress, with the time to failure being determined for each stress level. General technical literature and product data sheets seldom provide a complete description of a material s behavior prior to rupture. It should include the development of any crazing and stress whitening, its strain-time... 

When an engineering plastic is used with the structural foam process, the material produced exhibits behavior that is easily predictable over a large range of temperatures. Its stress-strain curve shows a significantly linearly elastic region like other Hookean materials, up to its proportional limit. However, since thermoplastics are viscoelastic in nature, their properties are dependent on time, temperature, and the strain rate. The ratio of stress and strain is linear at low strain levels of 1 to 2%, and standard elastic design... 

For elastomers, factorizability holds out to large strains (57,58). For glassy and crystalline polymers the data confirm what would be expected from stress relaxation—beyond the linear range the creep depends on the stress level. In some cases, factorizability holds over only limited ranges of stress or time scale. One way of describing this nonlinear behavior in uniaxial tensile creep, especially for high modulus/low creep polymers, is by a power... 

Most pigmented systems are considered viscoelastic. At low shear rates and slow deformation, these systems are largely viscous. As the rate of deformation or shear rate increases, however, the viscous response cannot keep up, and the elasticity of the material increases. There is a certain amount of emphasis on viscoelastic behavior in connection with pigment dispersion as well as ink transportation and transformation processes in high-speed printing machines (see below). Under periodic strain, a viscoelastic material will behave as an elastic solid if the time scale of the experiment approaches the time required for the system to respond, i.e., the relaxation time. Elastic response can be visualized as a failure of the material to flow quickly enough to keep up with extremely short and fast stress/strain periods. 

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